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A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
8 lbs peanuts, 1 lb almonds, 2 lbs raisins
6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
 one year ago
 one year ago
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
 one year ago
 one year ago

This Question is Closed

jim_thompson5910Best ResponseYou've already chosen the best response.0
Start off by defining variables
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
That they add up to 11 pounds haha
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
good, so x y and z add to 11, which means x+y+z = 11
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
that's one equation
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
But then we have to factor in how much they cost..
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
so like, 1.50x+3.00y+1.50=21..
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
Haha Okey you already said that x.x my bad
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
1.50z* I meant btw haha. I get that indeed.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
close, you mean to say 1.50x+3.00y+1.50z=21 but you got it
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
And don't forget twice the peanuts!
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
that's your 2nd equation
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
twice the peanuts as what?
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
it says, the recipe calls for twice as many peanuts as almonds O.o
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
good, so the equation for that is?
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
knew it was wrong x.x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Amount of peanuts = 2 times (amount of almonds)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
y = 2 times x or just y = 2x
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
oh pshh I should have thought of that x.x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
you can use them to solve for x, y and z
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
I'll get you started
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
Lol I can't because I'm stupid, But smart people definitely can haha
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
x+y+z = 11 x+2x+z = 11 3x+z = 11  1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
where are you lost?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
oh okay ! I see now, sorry it's really late and I'm super tired :/
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
so you have 3x+z = 11 7.5x + 1.5z = 21 now
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
solve the first equation for z to get this 3x+z = 11 3x+z  3x = 11  3x z = 11  3x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Since z = 11  3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11  3x) = 21 Solve for x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
oh wait, i made a variable mistake...i switched x and y one sec
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Let me fix real quick
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
I was thinking that haha x) ..
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
uhh ? your comment disappeared .. :o
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11  3y  1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11  3y) = 21 Solve that last equation for y
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Solve 6y + 1.5(11  3y) = 21 for y
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
Aw man I have to go to bed soon I'm dead tired x.x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
What do you get when you solve that equation for y
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
ergh I dunno x.x I'm brain dead
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Then give it a break, get some sleep and you'll tackle it in the morning
 one year ago

MeganDarlingBest ResponseYou've already chosen the best response.1
Oh no I keep losing connection >.<
 one year ago
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